As nations progress, the impact of climate change on food prices becomes increasingly substantial. While the influence of climate change on the yields of major agricultural products is widely recognized, its specific effect on food prices remains uncertain. This study delves into the impact of the North Atlantic Oscillation (NAO) index, a well-established climate indicator, on global food prices. To accomplish this, a robust bivariate Hurst exponent (robust bHe) is applied. The study employs a sliding windows approach across various time scales to produce a color map of this coefficient, presenting a time-varying version. Furthermore, variable-lag transfer entropy with a sliding windows approach is utilized to discern causal relationships between the NAO index and international food prices. The findings reveal that significant increases in the NAO index are correlated with noteworthy upswings in various international food prices over both short and long-term periods. Additionally, variable-lag transfer entropy confirms the causal role of the NAO index in influencing international food prices.